Generating elements of the algebra of block-symmetric polynomials on the product of Banach spaces ℂs.

The paper contains a description of generating elements of algebras of block-symmetric polynomials on finite and infinite ℓ_p-sums of spaces ℂ^s, s ∈ ℕ. In the case of a finite sum and s > 1 there are no algebraic bases in these algebras and we propose explicit formulas for algebraic dependencies between generating elements. [ABSTRACT FROM AUTHOR]